Vertical Accelerations in Prestressed Concrete Tanks

Vertical accelerations of circular cylindrical tanks and their contents cause hoop forces in the tank walls. The hoop forces caused by hydrodynamic fluid pressure are additive to those caused by hydrostatic fluid pressure; earthquake‐resistant design of tanks should therefore consider the combined fluid pressure. The design of a prestressed concrete tank wall must be such that under combined hydrostatic and earthquake‐induced hoop forces either: (1) The concrete does not crack (if leaking is not permitted); or (2) the stress in the prestressing wires remains below $0.7f_{\mathrm{pu}}$ (if minor leaking during the earthquake is permitted). Since under both of these criteria the tank wall materials remain practically elastic, the earthquake‐induced hoop forces should be based on elastic acceleration response spectra. This paper presents a normal mode solution for a neoprene pad supported, cylindrical, prestressed concrete tank filled with an inviscid and incompressible liquid subjected to vertical accelerations. The solution, which gives the natural modes and frequencies and the load participation factors, is used to compute the hoop forces caused by the hydrodynamic fluid pressure.